What is the reasoning of the 2 different minhagim (traditions) on what bracha to say on matzah when its not Peasach?
The Halacha is fairly clear about how to treat various categories of grain product:
What's far less clear is exactly what fits into which category. If, for instance, you consider cheerios to be #3, then you'd have to wash, make hamotzi, and bench on them if you treat them as your morning meal. (This is, I'm told, in fact the opinion of Chicago's Dayan Feurst.) The common practice is otherwise only because we categorize cheerios as #2.
The question here is our definition of "bread", category #1. Sephardic opinions have a very limited definition (many Ashkenazic challahs -- with their egg, oil, and vanilla, may not qualify for Sephardim), Ashkenazim have a broader definition. So it's no surprise that Sephardim think matza is a cracker when not Passover, but Ashkenazim say it's bread.